There must be something like 25 musicals on around the West End now. This makes the more serious-minded hang their heads in despair. They may very well be right, but to cheer themselves up they could go to see Hairspray, the 26th musical in town. It’s preposterous, but preposterously enjoyable.

Originally a film by John Waters, it then became a musical, which in turn inspired this year’s film remake with John Travolta. Here is a new production of the 2002 musical version, which mercifully retains much of Waters’s distinctive sensibility. His attitude to the minutiae of American trash-pop culture is oddly reminiscent of John Betjeman’s to Metroland: a kind of fastidious scorn mixed with real affection, a mixperfectly understood and embraced by the director, Jack O’Brien. Much of the humour here is in the tacky little details, such as the hot-dog stand bearing the legend “Fun on a Bun!”.

The plot is roughly the Cin-derella myth transplanted to 1962 Baltimore. Tracy Turnblad is the fat girl who longs to capture the heart of school hunk Link Larkin. But Link is dating the pretty, thin and vile Amber Von Tussle. Tracy, however, through sheer determination and friendship with the “col-oureds”, learns to strut her ample stuff very funkily indeed, and wins a place on the Corny Collins TV dance show. But she also has a social conscience – “If I was president, I’d make every day Negro Day!” – and wants the Corny Collins show to embrace integration and feature her new friends. Aryan Amber and her even more evil mother, Velma, scheme against Tracy every step of the way.

The story’s pretensions to having a serious message are a little dubious, but allow for some great dancing. None of the cracker boys (“racist word for ‘white man’” – Webster’s Dictionary) can match the astonishing snake-hipped jive of lead dude Seaweed J Stubbs (Adrian Hansel), whose moves attract the attentions of alabaster-skinned Penny: “In my ivory tower / Life was just a hostess snack / But now I’ve tasted chocolate / And I’m never going back!” The show’s cheerfully insensitive scattering of words we find embarrassing nowadays, such as “negro” and “coloured”, is bizarrely refreshing. Waters’s serious point here, if he has one, might be that there is Racism and there is racism. And the second, paltrier sort is best blown away by laughter.

Leanne Jones, as Tracy, dances her bobby socks off, and sings with a voice of outstanding warmth amid a lot of painful though comical shrillness; and Ben James-Ellis makes a very likeable Link. As my invaluable companion for the evening, Miss Katie Holland, 8, pointed out, he was previously a finalist in Any Dream Will Do and clearly has musical-star quality. (I would never have known but for Katie.)

Tracie Bennett makes a lavishly grotesque Velma Von Tussle, bravely sporting make-up to look like a hard-faced old bag, teetering around on canary-yellow stilettos, spewing fake winsomeness and real bile. But at the heart of this essentially teenage trash comedy, it is a number by Tracy’s parents that steals the show. Mel Smith, his features more and more, er, tired with every passing year, is an appealingly kindly dad, Wilbur Turnblad, while Michael Ball is clearly having a ball as Tracy’s mountainous mother, Edna (played by Divine in the original movie). Their duet, You’re Timeless to Me, a hymn to enduring lust far into saggy, baggy middle-age, got the night’s loudest applause.

We were actually singing the finale as we stepped out into the street: “ ’Cause you can’t stop the motion of the ocean, or the rain from above . . .” Who says musicals can’t be profound?

Shaftesbury Theatre, WC2